A New Approach to Formal Language Theory by Kolmogorov Complexity

We present a new approach to formal language theory by using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic context-free languages and nondeterministic context-free languages. The use of the “incompressibility arguments” is illustrated by many examples. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity.